I am qualified to answer this question. To me, the courses are mutually exclusive, in that Stone Eagle is a winter course and Ballyneal will be open from about May until early November. Choosing one to join would depend on when and where you'd like to have a getaway membership. Palm Desert is very posh, with swimming pools and movie stars. Holyoke is rural and friendly, a place where people wave as they pass one another on the road.
The golf courses both have undulating fairways, sloped greens, and artistic bunker work. Stone Eagle is very scenic, with beautiful short and long range views throught the round. And as stated many times here, Stone Eagle is a pretty tough walking course, and members will use carts most of the time.
The big difference between the two is the quality of the real estate. Ballyneal is built on ideal land for golf, while Stone Eagle is built on a more challenging, but equally dramatic site. Ballyneal is built for walking, and that's real important.
Stone Eagle has a few limitations as a golf course, which were discussed here recently. Some of the downhill par 4s are similar, and most of the par 3s are downhill "drop shots". Ballyneal will be subject to fewer generalizations of this type, as the course is blessed with a great variety of holes.
I have played Stone Eagle many times now, and I love it. I look forward to playing each hole. I especially enjoy driving the ball there; it is a great tee shot course. Soon I'll get my first chance to play Ballyneal multiple times, to see how I really like the course. Apparently the course is still a little soft and slow, as the grass needs to mature for a season or so before the desirable firm and fast conditions can be attained. Today my greatest concern is whether the course will be hard enough to satisfy low handicap golfers. At 7000 yards at 3700 feet elevation, the course is both wide and short for the good players. But the course features remarkably sloped greens and lots of uneven lies in the fairways, so the course theoretically should protect par well, especially when the turf firms up and the wind blows. I'll know a lot more in a couple weeks.
Feel free to ask further questions here or by IM.